JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. D7, PAGES 8845-8854, APRIL 20, 1997
Refraction and atmospheric photochemistry
M. Balluch and D. J. Lary
Centre For Atmospheric Science, Cambridge University, U.K.
Abstract. A new model for calculating the effects of refraction is introduced.
This model was invented independently of the one described by DeMajistre et al.
[1995], but it is shown that the two models are analytically equivalent. However, the
numerical implementation of the model introduced here is vastly more economical
and efficient than that of the model by DeMajistre et al. This is because the
two differential equations solved numerically by DeMajistre et al. have been
solved analytically for the new model, prior to the numerical implementation,
which reduced them to only one simple expression. The effects of refraction on
stratospheric chemistry calculated with this new model are shown to be greatest in
the polar lower stratosphere close to the onset and completion of polar night. The
main effect is to change the shape of the seasonal cycle of reactive species produced
by photolysis such as NO, NO2, OH, HO2, C1, C10, Br, and BrO during the onset
and completion of polar night.
Introduction
Recent developments in measurements of photodis-
sociation crosssections and photodissociation rates have
stimulated further improvements of photochemical mod-
eling. One such improvement has been the inclusion of
effects of atmospheric refraction of the solar beam [An-
derson and Lloyd, 1990]. Refraction is only important
for large solar zenith angles. However, it is the polar
springtime with its large solar zenith angles that has
attracted much attention lately in connection with the
formation of the so-called ozone hole. Therefore the ef-
fects of refraction on the photochemistry in the lower
stratosphere merit a detailed investigation.
In the following, a new refraction model will be intro-
duced, which is particularly suitable for use in the new
radiation model described by Balluch [1996], but it can
also be used in models with more commonly used coor-
dinate systems. This new refraction model will be com-
pared with another refraction model introduced inde-
pendently by DeMajistre et al. [1995]. It will be shown
that the model introduced here offers an improvement
to the model by DeMajistre et al. [1995]. Although
the two models are based on the same idea and are an-
alytically equivalent, the model introduced here makes
use of the coordinate system, which was introduced by
Balluch [1996] for the radiation equation, to simplify
the refraction equations considerably.
In the next section the new refraction model will
be deduced and compared to that of DeMajistre et al.
[1995]. Further, the effects of atmospheric refraction on
Copyright 1997 by the American Geophysical Union.
Paper number 96JD03399.
0148-0227/97/96JD-03399509.00
lower stratospheric photochemistry, with particular em-
phasis on the onset and completion of the polar night,
will be discussed.
Refraction Model
In the following section the model for refraction as
used for the calculations in this article will be described.
This model was invented independently of the one de-
scribed by DeMajistre et al. [1995]. It will be shown
that the two models are actually analytically equiva-
lent. To show this equivalence as well as to introduce
the model mathematically in an easy to follow, deduc-
tive way, we will start our deduction with equation (6)
from DeMajistre et al. [1995].
Basic Mathematics
DeMajistre et al. [1995] ended the derivation of their
model with the following two equations
dy p
: --- (1) dx H
dp_ () c9 (2) z--  0y
These equations describe the bent solar beam as a
function y(x) in Cartesian coordinates. Here p is the
conjugate momentum to the generalized coordinate y,
while x plays the role of the time in the Hamilton for-
malism. There is no z coordinate, since an incoming
beam in the (x, y)-plane will not be bent out of this
plane, because it was assumed that , the refractive
index of the atmospheric air, is only a function of al-
titude. Hence the z coordinate dependency can be re-
moved. The Hamilton function H is
8845

8846 BALLUCH AND LARY: REFRACTION AND ATMOSPHERIC PHOTOCHEMISTRY
H(x, y, p) - -V/ 2 - fo 2 (3) and
Equations (1) to (3) were derived by DeMajistre et al.
[1995] by minimizing the time used by light traveling
from one point to another and applying the Hamilton
formalism to the problem. The authors then integrated
these equations numerically to calculate the direct solar
beam when bent by refraction, referred to as the bent
solar beam in the following.
We want to proceed from this point by taking more
advantage of the assumption that  is a function of
the distance to the center of the Earth, r, only, i.e.,
 - (r). For such a situation it might be advanta-
geous to introduce polar coordinates (r, 0) instead of
Cartesian coordinates (x, y) (see Figure 1). Let us also
introduce the angle c as the angle between the tangent
of the bent solar beam and the line through the center
of the Earth, i.e., the center of the Cartesian coordinate
system (Figure 1). This angle a is called the apparent
solar zenith angle.
We can now represent the bent solar beam as c -
c(r). For that purpose, we need to transform the above
equations into the new coordinate system (r, 0) and ex-
press the derivatives with respect to r as the time pa-
rameter along the bent solar beam. It is easy to prove
that equation (2) becomes
dp _ qt tan 0 dqt dr - - H - go tan 0dr (4)
From Figure 1 it is obvious that
dy
: tan(0 - a) (5) dx
With equation (1), this leads immediately to
H tan a - p
tan0 - (6) H-q-p tana
Y
Figure 1. Definition of polar coordinates r and 0 and the
apparent solar zenith angle a. The size of the Earth and its
atmosphere are totally out of proportion to make the defini-
tions clearer.
tanc- go+Htan0 H - go tan 0 (7)
Furthermore, with equations (1), (3), and (5), we can
deduce
go - qt sin(0- a) (8)
With equation (3) it immediately follows that the Hamil-
ton function becomes
- cos(0 -
Equations (4) and (8) are essentially the new equations
(2) and (1), respectively. And equation (9) substitutes
for equation (3). We can therefore proceed meaning-
fully by combining the two equations (4) and (8) by
taking the derivative of equation (8) with respect o r
and equating that to the righthand side of equation (4).
With a bit of reshuffling and the use of equation (7), we
arrive at
d (O - a) i dgt
= tan a (10) dr ß dr
This equation is remarkable because the dependency
on p of the leRhand side has disappeared, effectively
reducing the original system of equations (1) and (2) to
describe the bent solar beam, to only one equation (10)
to describe the same bent solar beam. Next, considering
that
tan 0 - y (11)
we can derive
dO 1
-- = -- tan a (12) dr r
With the help of that equation we can now write the
equation for the bent solar beam
da 1 1 dqt
= -- tan a tan a (13) dr r ß dr
Balluch [1996] introduced a radiation model that uses
a new coordinate system (r, p, q), which drastically sim-
plifies the radiation equation. The coordinate q is de-
fined as the tangent of the local azimuth of the line of
sight times the cosine of a. In our application, for the
direct solar beam, the azimuth is zero by definition, and
therefore q = 0. The coordinate p is defined as
p- r sin c (14)
From that we deduce
dc dP =sin a + r coS a dr r -- (15)
and with the use of equation (12) the new equation
describing the bent solar beam becomes
dp p d
d- = ß dr (16)
which would simply be obtainable from Snell's law as
well.

BALLUCH AND LARY: REFRACTION AND ATMOSPHERIC PHOTOCHEMISTRY 8847
This we can integrate analytically and arrive at
p(r) - p(rout) q (rout) (17)
This is the new equation for the bent solar beam with
refraction. Without additional assumptions we have re-
duced the system of differential equations, equations (1)
and (2) as used by DeMajistre et al. [1995], to a very
simple expression, equation (17), describing exactly the
same thing.
Let us assume that the atmosphere is represented by
a number of discrete spherical shells of constant physical
properties like density and temperature (and therefore
refractive index ß as well), as it would be in a numerical
model. At each interface between the layers we could
apply Snell's law to calculate refraction. Let's give the
outside a superscript 'plus' and the inside a superscript
'minus'. Then we have in our terminology
p+ sin a +
= = p- sin c-
If we consider now that the atmosphere consists of
a number of such shells and interfaces between them,
we arrive exactly at equation (17). In contrast o what
appears to be a claim of OeMajistre et al. [1995] (at
the beginning of the section 2' Refraction Model), the
Hamiltonian approach and Snell's law are exactly the
same in the discrete representation.
As can be seen in Figure 2, the bent solar beam is
now represented by steps of decreasing p values. To
calculate the optical depth r, we have only to add the
width of each of these \"p steps\" times the extinction
per length, a'
i,i+lT --  -- P,i+l -- F+I -- Pi,i+l
(xo)
where ai,i+ is the average value of a between radius
ri and radius ri+.
Method of Solution
According to Figure 1, c(r) is the apparent solar
zenith angle at r. We still need to set this in relation to
the true solar zenith angle fi, which is the angle between
the solar beam and the zenith if there was no refraction,
i.e., if the solar beam was a straight line. The basic ob-
servation to start from is that for each shell (i, i q- 1),
i.e., on any straight line, fi changes exactly as c,
- -
where c/+ is the outer value of c at interface ri and c- is
the inner value of c at interface ri. Over each interface
i, however, only c changes, according to equation (18).
Consequently, we can add up equation (20), and since
Cout - flout outside the outermost shell, we arrive at
j-1
]j -- (outq--(./++l--(?) (21)
i=1
That means for a given value of aout, we can calcu-
late a true solar zenith angle /?j at any radius rj. In
practical applications we will only know/?j and want to
calculate aout in order to use equations (17) and (19)
for solving the radiation problem. For that we have to
solve equation (21) for aout with a shooting procedure.
For this shooting procedure we use a first guess for aout
and then integrate quation (21) to yield a j, which we
can compare to the true solar zenith angle we want to
achieve. Depending on whether the solution/?j of equa-
tion (21) with our guess for aout is larger or smaller than
the true solar zenith angle we want to reach, we choose
a better guess for aout, larger or smaller than the for-
mer, to yield a better solution/j of equation (21). This
procedure we repeat iteratively until j and the true
solar zenith angle we want to achieve agree to sufficient
accuracy. For the first guess, we could choose aout, as it
would be without refraction. This shooting procedure
becomes necessary because all a values depend on the
outermost a, i.e., aout, according to equation (17).
There are, however, a few more problems to consider.
The above is strictly true only for solar zenith angles
;, where the bent solar beam hits r 3 directly, without
passing first through a tangent point in the atmosphere,
i.e., a point of closest proximity to the Earth, before
reaching the altitude of interest. Also, for certain j, r3
might actually lie in the shadow of the Earth, i.e.,not
in direct sunlight.
i-2,i-I
Pi- l,i
Pi,i+l
Pi+l,i+2
r+
Figure 2. The bent solar beam in discrete approximation i
coordinates r and p is represented by steps of constant p
values (thick line segments). Over the shell interfaces the
refractive indices change discontinuously. The p values
change correspondingly, according to Snell's law (see
equation I17] or I18] ).

8848 BALLUCH AND LARY: REFRACTION AND ATMOSPHERIC PHOTOCHEMISTRY
We can calculate the true solar zenith angle for both
cases. For calculating theedge of the Earth's shadow, 98
i.e., the terminator, we only need to calculate the bent 94
solar beam that just about grazes on the surface of the
Earth, i.e., the bent solar beam which has a tangent 92
point at zero altitude. For calculating the bent solar
beams which have a tangent point altitude of exactly !90
the altitude of interest, i.e.,those bent solar beams that .
 88
end tangentially for each rj, we only have to solve qua- _
tion (21) for aJ- - 90 ø. All these cases ofcalculating o bent solar beams with tangent points at given altitudes 
can be solved irectly with only one integration of equa- 
tion (21). It is easy to show that the true solar zenith
angle for the case of c - 90 o at rj is 82
max _. Oou t 80 78
ß
ri+ x i,i+ 1
- arcsin (rJ qJ-x'J )) (22) ii,i+l
For all j such that fij > / 'dmax the solar beam will
/?dmax pass its tangent point. For all j such that fij < ,j ,
the solar beam will not have a tangent point at all.
This is important because if there is a tangent point,
equation (21) does not really apply. However, since
the solar beam is symmetric with regard to the tangent
point, for the cases with a tangent point, we have to
add those p steps on the other side of the tangent point
twice in the sum of equation (21). In that way we can
calculate the true solar zenith angle for the terminator
(out
ß
+ i(arcsin(rNN-I'N) ri+  i,i+ 1
_ arcsin (rNqN-,N)) rii,i+
q- 2(arcsin(rNqtN-'N) ß . ri+l !Iti,i+l
- arcsin (rNN-X!N)) (23) rii,i+l
where N is the largest index, i.e.,rs is the surface of
the Earth. For all j such that j > /nax, rj is in the
shadow of the Earth, i.e.,not in direct sunlight. For all
j such that j < ax, rj is in direct sunlight.
What remains to be shown is that aout is actually
a monotonic function of , so that the shooting proce-
dure converges, i.e., that we can guess from the error
in  to a better boundary value aout in an efficient and
deterministic way. Figure 3 shows the relation of  and
aout with and without refraction for a typical midlati-
tude profile at an altitude of 20 km and a wavelength
of 400 nm. The turning point of the curve is exactly
400nm, outer boundary of alpha versus true solar zenith angle
, , , , , ! ,
48%191
.''efraction
no refrachon
, , , , ; , 78.5 7 79.5 80 80.5 1 8 .5 82
alpha_out [deg]
Figure 3. The true solar zenith angle ,6 as a function of tzot
for an altitude of 20 km and a wavelength of 400 rim. The
lower branch corresponds to solar beams without tangent
points, the upper branch to solar beams with tangent points.
The changes of the upper branch are shown for with or
without refraction, and for 48 or 191 spherical shells in the
calculation with refraction.
at / = dmax. We can see that if we split the prob-
lem into one with/ > dmax and/ < dmax, as it is
possible with the help of equation (22), we indeed have
a monotonic relationship between/ and aout for each
case separately.
In Figure 3 we can also see the difference with and
without refraction. The two slightly different curves for
the case with refraction are derived with 191 and 48
discrete spherical shells, as indicated in the Figure. As
can be seen on the curves with realistic refractive index
(realistic refractive index for air from Birch and Downs
[1995]), the monotonicity can only be assured above a
certain scale, depending on the number N of shells in
the calculation. Even for 16 shells, though, the error in
Cout is below 5 x 10-4/.
Figure 4 shows the difference between apparent and
true solar zenith angle at a wavelength of 175 nm. The
difference increases to more than 1.3 ø. However, for a
solar zenith angle below 850 , the difference is less than
0.20 . The enveloping of the contour lines at the largest
true solar zenith angles gives the terminator.
The radiation model used for the results shown in the
next section is the one from Balluch [1996] coupled with
this refraction model. It should also be noted that the
extension of this model for refraction from only applying
to the direct solar beam to applying to all scattered
and reflected beams is straightforward as long as all
scattering processes are isotropic. All beams defined by
constant p values would just have to be exchanged to p
step functions as in Figure 2. However, for anisotropic
scattering the dependency of the refraction equations on

BALLUCH AND LARY: REFRACTION AND ATMOSPHERIC PHOTOCHEMISTRY 8849
8O
7O
6O
5O
ß 40
3O
2O
10
175nm, difference between apparent and true solar zenith [deg]
i i i i i i
.4
.7,
80 82 84 86 88 90 92 94
true solar zenith angle [deg]
shade
of Earth
78 98
Figure 4. The difference between apparent and true solar
zenith angle for a wavelength of 175 nm. The rightmost curve
represents approximately the terminator with refraction,
which is 1.30 further to the right han the terminator without
refraction would be.
the/ coordinate, as discussed above, cannot be removed
so easily.
The method outlined can also be used with more com-
monly used coordinate systems for the radiative transfer
equation, e.g., optical depth and polar and azimuthal
angle. This may be achieved by calculating the optical
depth with the help of equation (19).
Impact on Photochemistry
Refraction has its greatest effect on stratospheric
chemistry in the polar lower stratosphere. In order
to asses the impact of refraction alone on the chem-
istry of the lower stratosphere, a set of chemical box
model calculations was perfomed. These simulations
were for 50 mb (20 km) at a range of latitudes between
700 and 850 . The simulations started in autumn and
went through to the following spring. The temperature
was artificially kept at 205 K, so that the variations in
the chemistry would be due to the motion of the Earth
relative to the Sun alone.
Photochemical Model Description
The numerical model used was the AUTO CHEM model
described by Lary et al. [1995, 1996], Lary [1996] and
Fisher and Lary [1995]. The version of the model used
in this study contains a total of 81 species. Of these,
74 species are integrated, namely; O(1D), O(3p), 03,
N, NO, NO2, NO3, N205, HONO, HNO3, HO2NO2,
CN, NCO, HCN, C1, C12, C10, C1OO, OC10,
C1NO2, C1ONO2, HC1, HOC1, CH3OC1, Br, Br2, BrO,
BrONO2, BrONO, HBr, HOBr, MeOBr, BrC1, H2,
H, OH, HO2, H202, CHa, CHa, CHaO2, CHaOOH,
CHaONO2, CHaO2NO2, HCO, HCHO, CF3, CF30,
CF302, CF3OOCI, CFaOH, CFaOOH, CFaOONO2, F,
F2, FO, FO2, F202, COF2, FCO, FCOO, FCOOH,
FC(O)O2, FNO, FONO, FO2NO2, HF, CH4, CHF3,
CH3Br, CF2CI2, N20, CO. The remaining seven species
are not integrated and not in photochemical equilib-
rium, namely: CO2, H20, 02, N2, HCI(s), H20(s),
HNO3(s). The model contains a total of 438 reactions,
287 bimolecular eactions, 43 trimolecular eactions, 65
photolysis processes, and 43 heterogeneous reactions.
Refraction acts to extend the time per day for which
light is present. As a result, when refraction is included
in a numerical simulation we generally have higher con-
centrations of those species which are produced by pho-
tolysis.
The following sections will consider, in turn, the ef-
fect of refraction on various chemical species. The time
period when refraction has the biggest effect is close
to the onset and completion of polar night. However,
the effects of refraction are also visible at much lower
latitudes.
03
The effect of refraction on the ozone concentration is
relatively small below 45 km. When refraction is in-
cluded, the abundance of shortlived species uch as C1,
Br, OH, and NO are increased, particularly close to
the polar night boundary. This is because the period
of time for which photolysis occurs is extended. As a
result, when refraction was included, the ozone loss in-
creased below 45 km, reaching a maximum additional
loss of-0.5% over 7 days at around 40 km between 560
and 640 latitude. Figure 5 shows the percentage change
in 03 over 7 days due to refraction as a function of al-
titude and latitude at the solstice. The additional loss
is not restricted to the region close to the polar night
boundary but also extends into the tropics. Above ap-
proximately 48 km there is an increase in 03 produc-
tion due to increased photolysis, reaching a peak of ap-
proximately 10% at 650 latitude. Figure 5 shows that
the high-latitude boundary of the region affected by re-
fraction mirrors the polar night boundary, which moves
poleward with increasing altitude.
Nitrogen Species
As can be seen in Figure 6, the enhancement in the
NO and NO2 concentration is significant (and lasts for
several days) close to the polar night boundary. How-
ever, small changes also extend well into mid-latitudes.
The region of increase in NO on the day side of the polar
night boundary, which is greater than 10%, is consider-
able and extends over a few degrees of latitude centered
on approximately 660 between 10 and 30 km. A similar
response is observed for NO2.
After polar night at a latitude of 700 the enhancement
in NOx is greater than 10% for a few weeks. The NOs
enhancement during polar night itself is not very signif-

8850 BALLUCH AND LARY: REFRACTION AND ATMOSPHERIC PHOTOCHEMISTRY
3O
5O
(D :5o- \"0
:::3 -
lO
30
O percentage increase
40 50 60 70 80
....
............. , _ ,_._....,,.. , - --,...- ., :,::...: : . : .. ..........::::.. - :: :.,.  ::.,:.'.-.':::.*:.,'...-'..::::,i . . ........- \"\"*'\"<\"-' ' .' -':, ::::  .... : ''-'-  \",.'.'.'..-: . .
........ ......
..........
40 50 60 70 80
Latitude
5.00
.............
...........................
..............
2.00 '\"\"\":'** * :'* * .-- ß:**
1.00 \"'\"'\"'\"'\"\"\"'\"'*\"\" '\" ':' '\ 0.50
:::::::::::::::::::::::::
0.05 ::: 0.01 ...ß o.o
-0.50 :. .....................
Figure 5. The percentage change in 03 over 7 days
due to refraction as a function of altitude and latitude
at the solstice.
icant as during this period the NOx concentrations are
negligible. The effect of refraction on the HNO3 con-
centration is small and restricted mainly to the upper
stratosphere and mesosphere.
As the production of HONO is mainly due to the
reaction of OH with NO, there is a considerable en-
hancement in the HONO concentration. The same is
true for HOeNO2 which is produced by the reaction of
HO2 with NO2.
Hydrogen Species
As can be seen in Figure 7, the enhancement in the
H, OH, HOe, CHa and HCHO concentration is signif-
icant and lasts for several days close to the onset and
completion of polar night. The region of increase in H,
OH, HOe, CHa and HCHO extends over a few degrees
of latitude centered on approximately 66 o and occurs
throughout the stratosphere. Refraction has slightly
enhanced methane oxidation.
In the case of H202, an enhancement in HO caused
by photolysis produces more H202, but in turn, H202
is also photolyzed. This generally results in a net re-
duction in
Chlorine Species
As can be seen in Figure 8, the enhancement in the
C1 and C10 concentration is significant and lasts for
several days close to the onset and completion of polar
night. At a latitude of 700 the enhancement in C1 lasts
for about a month. The region of increase in C1 and
C10 extends over a few degrees of latitude centered on
approximately 660 and occurs throughout the strato-
sphere. In the lower stratosphere close to the polar
night boundary the increase in C10 leads to a notice-
able increase in C120 of up to 20%. However, at lower
latitudes, due to its rapid photolysis including refrac-
tion reduces the C1202 concentration.
Owing to the very rapid photolysis of HOC1, includ-
ing refraction reduces the HOC1 concentration in the
lower stratosphere. In the upper stratosphere the in-
creased abundance of HOz and C1Oz means that the
enhanced production of HOC1 outweighs its enhanced
photolysis and there is a net increase in HOC1.
In the lower stratosphere close to the polar night
boundary the increased abundance of NO2 and C10 due
to refraction leads to an enhanced C1ONO2 concentra-
tion. This enhancement is most noticeable in the re-
covery period in early spring. However, above about 20
km the enhanced photolysis of C1ONO2 leads to a net
reduction in its concentration, an effect which extends
to much lower latitudes.
The effect of refraction on the HC1 concentration is
small.
Bromine Species
As can be seen in Figure 9, the enhancement in the
Br and BrO concentration is significant (and lasts for
several days) close to the onset and completion of polar
night. It is an enhancement that extends throughout
the stratosphere close to the polar night boundary.
Owing to its very rapid photolysis, including refrac-
tion reduces the concentration of BrC1. Also owing to
its very rapid photolysis, including refraction reduces
the HOBr concentration for several days close to the on-
set and completion of polar night. However, during the
polar night itself the HOBr concentration is increased.
This is a reflection of the increased HO2 and BrO con-
centrations.
The increased abundance of NO2 and BrO due to
refraction leads to a considerable enhancement of the
BrONO2 concentration (of up to 20% and more). This
enhancement is most noticeable in the recovery period
in early spring.
The two main sources of HBr are the reactions of Br
with HO2 and HCHO. The increases in the Br and HO2
concentrations therefore lead to an increase in the HBr
concentration when refraction is included.
Summary
A new model for calculating the effects of refraction
has been introduced. This model was invented indepen-
dently of the one described by DeMajistre et al. [1995],
but it is shown that the two models are analytically
equivalent. However, the two differential equations that
were solved numerically by DeMajistre et al. [1995]
are solved analytically here to yield a vastly simplified
analytical expression. It is this simplified expression
which is numerically implemented in the model intro-
duced here.
The effects of refraction on stratospheric chemistry
have been considered and are shown to be greatest in

BALLUCH AND LARY: REFRACTION AND ATMOSPHERIC PHOTOCHEMISTRY 8851
NO percentage increase
30 40 50 60 70 80
50_1 [ [ [ [ I [ [[ [ I [ [ ,._
30 40 50 60 70 80
Latitude
N20. percentage increase
30 40 50 60 70 80
30 40 50 60 70 80
Latitude
HN03 percentage increase
30 40 50 60 70 80
50
E
'___. ..:.:.......z:
1
30 40 50 60 70 80
NO2 percentage increase
30 40 50 60 70 80
 20
 10, 5 20 2
-1
101   [ [ I' [ i i ill fll i i i [ I I I I [ I I I f
30 40 50 60 70 80
Latitude
HONO percentage increase
30 40 50 60 70 80
E
Q) 30
10 '\"<'+:'\"\" \"\"\"'\"!{
20 ,....,,.. 5 x  2
lO
30 40 50 60 70 80
Latitude
30
HONO percentage increase
40 50 60 70 80
,..,,:..-:;?,:.-.-'. 5.00 :::::::::::::::::::::::::::::::::::
r'\"\"'\"\" ': /'. ;, 2 0.50 :::---':':.'------ '  :i O. 10 ......................
:!.i:::::::!: , ,0.01 
---.----..,....-& ,o. o5%
.2. oo,------:.:.--.,.. :-j!
- 10. O0 ::::::::::::::::::::::
30 40 50 60 70 80
Latitude Latitude
Figure 6. The percentage change in noon NO, NO, NO, HONO, HNO3 and HONO2 over 7
days due to refraction as a function of altitude and latitude at the solstice.

8852 BALLUCH AND LARY: REFRACTION AND ATMOSPHERIC PHOTOCHEMISTRY
H percentage increase
30 40 50 60 70 80
E
(l) 30
ß  50 \"'\"'\"\"':'::-- .-.:
2100 1 :'\"\":\":'\"'\"::::'-\"--'- ---.. '
30 40 50 60 70 80
Latitude
3O
- ===================== ii..:'_...-' ',.':::  ..'-!::
.... , ._: ,,......,. . ...   ``::::::::::.`..:::::::::````:::..   .:... .. : ...:...`}3    :.``I\":    ..``.
................................................ '\"::..\"::' ' ''\"'\"\"'\"'\"'::'[' '.  : : .  !! x'\"\":'. . .,...'M,:i.:i
40-- ............................................. '\"\"' :-.:,,'\"I i :'\"':.'2.\"\".I1
 : ............................................. ============================================================
::::::::::::::::::d::ii:::':::::.::>:::::::::::::::::s:::::::.:::2::::>;s::::::::::\" '-'. A- .' ::::'-:::',- :::::
3O
HO percentage increase.
40 50 60 70 80
i i i
i i i
40 50 60 70 80
Latitude
CH percentage increase
30 40 50 60 70 80
, , , , , , , , , , , , , , ,
lO
30 40 50 6o 70 80
Latitude
OH percentage increase
30 40 50 60 70 80
30 40 50 60 70 80
Latitude
5O
 30
20
10
HO percentage increase
30 40 50 60 70 80
I I ! I I I I I I I I I I I I I I I I I I I I I I I I I I
,:.: ?:. 8:'.::::.;::::::::;
30 40 50 60 70 80
Latitude
HCHO percentage increase
30 40 50 60 70 80
I .:'i.'.'.! IIIjlllllllllll lll!llllllll
..... ß ':':':':':':':':':': ..... '\"':':':--:i :.:.:.:.:..-::.: x -,'.;.:-'-..'.:..-:...::::::::::::..:.::..::::.
....................... '-'\"\"'\"\"\"'\"\"'\"\"\"'i:::!il ø-'\"'\"'\"\"\"'\"''\"\"'':!
:[ ....................... ,_  ,  ,  ;::, ' ..........  ,, . :.:.. ,,::, !
'-'\"\"\"'-\"-'--' ....................................... i:-.'.'.-'g, .::::i::  i.: ............ \":':-, ' '.':iil
o F' ...................  :`:``:i..:..`...```..``......`:.... ::.
0,) 30 `...::ii:::......``.:::::` ...,,:,,.,.::....:::::: ..... '\"'\"'\"\"-'.\"--   ,- '::
-o I  ............................... \"- ' \"-, ' - ' \"' \"' \"' \" \"'\"\"':'\" 
.......... ..................... - '\" ',:':b'.'-., !:i:::'o'. ....................... :'\":_ ' : 'i
\"'\"'' ' ' \"\"'\":i ........................................... .::::-\"'\"\"'\"'\"'\"\"\"\"'\"'\"\":. .,...... .!
101    Ili Ill Ill ill ill I I t I I I I i I I
30 40 50 60 7'0 80
Latitude
-:-:-:-:-:-..-:-:-:-:-:-:-: .............
- 20.0'\"--:':'-':'------':;\".
\"'\"':\":\" ,'- ß ;-- - :' .': '!i
2.0 . i-':
...........
Figure 7. The percentage change in noon H, OH, H02, H202, CH3 and HCHO over 7 days due
to refraction as a function of altitude and latitude at the solstice.

BALLUCH AND LARY: REFRACTION AND ATMOSPHERIC PHOTOCHEMISTRY 8853
Cl percentage increase ClO percentage increase
$0 40 50 60 70 80 $0 40 50 60 70 80
5O 5O
20 1 0 20 1 0
5 5
2 2
1 I
30 40 50 60 70 80 30 40 50 60 70 80
Latitude Latitude
CI202 percentage increase CION02 percentage increase
30 40 50 60 70 80 30 40 50 60 70 80
 :::::::::::::::::::::::::::
10. 0 i?:i?:i??  40 ...........................
' [\"'  <\"\" ' ':'%:-...--. 0.5 ::::::::  o 0.5..,;:.,.:..,. D m ,'\" ',....  .: {ii::i':'\"'i\"'\"ii ;'qd 1.0 ........................ .' 1.0\" \"'\"'':' '::'\ ' ' , .
_o-1  .:!:i:i:i:i.':.'..'-%'-'.:!:::::.:!. -2 0 ':- . .. - :-; :':i::-.. ..:':':..:::....-::.::i::':.::i .... '..:*i.'.-':i.:..\".*.:*.:.'.\"*.:- ... '? .. ..... . . ... ':'' ':\ i ....  -0 1
::::::::::::::::::::::::::::::::::::: . :::::::::::::::: - i ;-! i:i:i ' -i ; i.'.-' i ;:i:i:::-:
*q..-.-':.-'.'.,',,.-' ,, ,.'.,,:: :: . , : . .-:,..:.::.,::.?-:...:-....::,-.--.,:-:::,:, .. . . . ::: : :: '::,:, - i? ) -5. o.i'\"':':\"\"\"::'\"'\"'-.----\"
,o, .... , .... , .... ,,?:?i!, .... ,,,, _1o.o ... ............... ß lO.O . .................... lO
30 40 50 60 70 80 30 40 50 60 70 80
Latitude Latitude
(D 30 \"0
::3
..
HCI percentage increase
30 40 50 60 70 80
. ........-..x.:.x-: *\":4':\"w;'.../i  ,'m .,,.:, -,.,:,..., ,, .. . ::. .{........:: :......:.. ... ..
 _- ........... 0, .'w,, ,,x,.-:-).:.ii ' \"'\"::'\":'\"\":'\"'\"\"
'1 i i i I i i i i i i i i I i i i i
30 40 50 6O 70 80
Latitude
HOCI percentage increase
30 40 50 60 70 80
0.10 \"'\"\":'\"':'
0.05 ,,..,..x.x
0.01 \"\"'\"\"' :\" : 0.01 1
-1.00 -zu ------
30 40 50 60 70 80
Latitude
Figure 8. The percentage change in noon C1, ClO, C1202, ClON02, HC1 and HOC1 over 7 days
due to refraction as a function of altitude and latitude at the solstice.

8854 BALLUCH AND LARY: REFRACTION AND ATMOSPHERIC PHOTOCHEMISTRY
Br percentage increase
30 40 50 60 70 80
.... ,,
,o .... ,.... ,.... ,....
30 40 50 60 70 80
Latitude
50 '-'-'-.--:':':-.---\"--::.. :...
0 =========================
3O
BrO percentage increase
40 50 60 70 80
! t  
-.......-.................
40 50 60 70 80
..
Latitude
Figure 9. The percentage change in nooii Br, BrO, HOBr and BrON02 over 7 days due to
refraction as a function of altitude and latitude at the solstice.
the region close to the polar night boundary. During
this period the concentration of species produced by
photolysis, such as OH, NO, C1 and Br, are considerably
enhanced. In the simulations presented here the effect
on ozone depletion due to the inclusion of refraction
was up to 0.5% over a 7-day period between two sim-
ulations, one which included refraction and one which
did not include refraction. The ozone loss was not re-
stricted to the iegion close to the polar night boundary
but also extended to low latitudes. If, however, there
are large regions of cold temperatures during the onset
and Completion of polar night the additional ozone de-
pletion could be larger than the results presented here.
In contrat, in the upper stratosphere and lower meso-
.,
sphere, increased photolysis leads to a considerable en-
hancement in the Oa concentration.
The main effect of refraction is to change th shape
o f the seasonal cycle of reactive species produced by
photolysis such as NO, NO2, OH, H02, C1, ClO,.Br, and
BrO during the onset and completion of polar night.
Acknowledgments. David Lary is a Royal Society Uni-
versity Research Fellow and wishes to thank the Royal So-
ciety for its support and J.A. Pyle for his helpful coopera-
tion. The Centre for Atmospheric Science is a joint initia-
tive of the Department of Chemistr y and the Department of
Applied Mathematics and Theoretical Physics. This work
forms part of the NERC U.K. Universities Global Atmo-
spheric modeling Programme.
References
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visible radiation field: Perturbations due to multiple scat-
tering, ozone depletion, stratospheric clouds, and surface
albedo, J. Geophys. Res.,-95(D6), 7429-7434, 1990.
Balluch, M., A new numerical model to compute photoly-
sis rates and solar heating with anisotropic scattering in
spherical geometry, Ann. Geophys., 1., 80-97, 1996.
DeMajistre, R., D. E. Anderson, S. Lloyd, P. K. Swami-
nathan, and S. Zasadil, Effects of refraction on photo-
chemical calculations, J. Geophys. Res., 100(D9), 18,817-
18,822, 1995.
Fisher, M., and D. J. Lary, Lagrangian four dimensional
variational data assimilation of chemical species, Q. J. R.
Meteorol. Soc., 1œ1(527) Part A, 1681-1704, 1995.
Lary, D. J., Gas phase atmospheric bromine photochemistry,
J. Geophys. Res., 101(D1), 1505-1516, 1996.
Lary, D. J., M.P. Chipperfield, and R. Toumi, The potential
impact of the reaction OH+C10-+HCI+O2 on polar ozone
photochemistry, J. Atmos. Greta., œ1(1), 61-79, 1995.
Lary, D. J., M.P. Chipperfield, R. Toumi and T. M. Lenton,
Atmospheric heterogeneous bromine chemistry, J. Geo-
phys. Res., 101(D1), 1489-1504, 1996.
M. Balluch, Centre For Atmospheric Science, Depart-
ment of Applied Maths and Theoretical Physics, Cambridge
University, Silver Street, Cambridge, England. (e-mail:
mgb@dam tp. cam .ac. uk)
D. J. Lary Centre For Atmospheric Science, De-
partment of Chemistry, Cambridge University, Lens-
field Road, Cambridge, CB2 1EW, England. (e-mail:
david@atm.ch.cam.ac.uk)
(Received April 18, 1996; revised October 11, 1996;
accepted October 11, 1996.)